However, in view of the duality between $H^1$ and $BMO$, we are able to give a meaning to the product as a Schwartz distribution. Moreover, this distribution can be written as the sum of an integrable function and a distribution in some adapted Hardy-Orlicz space. When dealing with ...
7. Note that each dataset is an independent subject, so the dotted lines in the graph have no real meaning only the values at the nodes to focus on. However, the datasets are organized by the number of samples from the smallest to the largest, revealing an increasing trend in CPU time ...
Despite its great scientific and technological importance, wall-bounded turbulence is an unresolved problem in classical physics that requires new perspectives to be tackled. One of the key strategies has been to study interactions among the energy-containing coherent structures in the flow. Such inter...
7. Note that each dataset is an independent subject, so the dotted lines in the graph have no real meaning only the values at the nodes to focus on. However, the datasets are organized by the number of samples from the smallest to the largest, revealing an increasing trend in CPU time ...
Ishiu [9] proved that the notions of Axiom A and <ω1-properness are in fact the same, meaning that, up to forcing-equivalence, they describe the same classes of quasi-orders. This also explained an earlier result of Koszmider [10] saying that Axiom A is preserved by countable-support...
In mathematics, the qualifier pointwise is used to indicate that a certain property is defined by considering each value. What is the meaning of pointwise? adverb. 1In the manner of a point or tip; in respect of points; with the point foremost or uppermost. 2Mathematics. With regard to ...
In Cartesian coordinates the equation of a line is, y=mx+n, wheremis the slope of the line andnits intercept with the y-axis. If the slope is positive the line is increasing meaning thatygrows along withx. Meanwhile, ifmis negative the line i...
For the interpretation of the various objects appearing, we refer to the rest of the paper, but the meaning such objects can also be deduced by comparison with (1), (2). Theorem Let (X,d,m) be an RCD(K,N) space, let F∈BVloc(X)m and let φ∈LIP(Rm). Then where we ...
pmGH convergence, meaning that a pmGH limit of a sequence of (pointed) {{\,\mathrm{RCD}\,}}(K,N) spaces is still an {{\,\mathrm{RCD}\,}}(K,N) m.m.s. The basic references for the theory of convergence and stability of Sobolev functions on converging sequences of {{\,\...
The goal of the present section is to understand the geometric meaning of the notion of turn, and to prove it independently of the choice of an isothermal coordinate system. A notion of turn of a curve was also introduced in the monograph of A. D. Alexandrov and V. A. Zalgaller. The...